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1 Weierstrass Institut für Angewandte Analysis and Stochastik 2 Institut für Mathematik Berlin 3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning problem refers to the case where the number of elements in each group is fixed to $N-k$. In the case $k=2$ it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case $k>2$ in the restricted problem and show that the vector of differences between the $k$ sums converges to a $k-1$-dimensional Poisson point process.

Mots-clés : Random Energy Model Poisson process Number partioning extreme values

Autor: Anton Bovier - Irina Kurkova -

Fuente: https://hal.archives-ouvertes.fr/


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